A026522 a(n) = T(n, n-2), where T is given by A026519. Also number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 2.

1, 2, 5, 13, 27, 76, 150, 434, 845, 2470, 4797, 14085, 27377, 80584, 156900, 462620, 902394, 2664276, 5205950, 15387670, 30114073, 89097932, 174609162, 517058502, 1014555607, 3006637946, 5906040623, 17514547015, 34438443075

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000
• Veronika Irvine, Stephen Melczer, and Frank Ruskey, Vertically constrained Motzkin-like paths inspired by bobbin lace, arXiv:1804.08725 [math.CO], 2018.

Crossrefs

Cf. A026519, A026520, A026521, A026523, A026524, A026525, A026526, A026527, A026528, A026529, A026530, A026531, A026533, A026534, A027262, A027263, A027264, A027265, A027266.

Programs

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k], T[n-1, k-1] + T[n-1, k-2] + T[n-1, k]]]]; (* T = A026519 *)
Table[T[n, n-2], {n,2,40}] (* G. C. Greubel, Dec 19 2021 *)

Sage

@CachedFunction
def T(n,k): # T = A026552
    if (k==0 or k==2*n): return 1
    elif (k==1 or k==2*n-1): return (n+1)//2
    elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
    else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
[T(n,n-2) for n in (2..40)] # G. C. Greubel, Dec 19 2021

Formula

a(n) = A026519(n, n-2).